Hi there and welcome
Sorry to hear you're having some NWs at the moment. Looking at your routine, I wonder if he may need a little more A time, especially if he's up and happy after 45mins? Although the av is 2hrs for 4mo, at 4.5months, we were actually working on transitioning to 2 naps and some of our A's were close to 2.5hrs. By around 5-5.5 months, we were down to 2 naps and doing much better. By around 5 months, the av A time is somewhere between 2-2.25hrs, so I wonder if you try adding another 10-15mins to his A, whether that will help him take longer naps?! I would probably work on 1 A at a time, starting with the morning nap and if you're worried about him getting overtired, try adding just 10mins and hold that for a couple of days before extending him more.
Your E's look good and milk is the primary source of food until 6 months and if you add solids too early, his gut is probably not ready for that and may cause even more night wakings. There is also the 4 month sleep regression, which may be contributing to the night wakings and usually with sleep regression, try and stay away from using AP and it will pass.
But I would probably work on extending naps and rather than letting him take a 4th catnap, I would probably do an earlier bedtime.
What do you think?